The present monographical set of notes is a first systematic attempt at answering the following fundamental question: What mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The author first proposes an axiomatization of the physics inspired notion of Einstein-Weyl causality and investigating the consequenes in terms of possible topological spaces. The mathematical level required of the reader is that of the graduate student conversant in mathematical physics. For physicists interested in applications, the most significant result is that the notion of causality can effectively be extended to discontinuum. (source: Nielsen Book Data)